Even with a few vigilantes in the MCU like Punisher and Daredevil, whom Marvel do own, there aren't so many of them that it's out of hand. There could be as many as there are vigilantes in the real world who take matters into their own hands. Isn't Punisher's identity known anyway? It would only really be DD who has a secret identity, and whether he keeps it secret from SHIELD is another matter.

A Civil War type of storyline won't work in the MCU for many of the reasons stated - no secret identities, a lack of vigilantes, Stark's anti government stance, and the fact that Thor is the only team member who hasn't been a government employee or contractor. I can't see Feige greenlighting a film of Fury chastising Odinson to fill out paperwork.

The idea of superhero registration, however, will probably be a major focus of the SHIELD tv show. The adulation given to the Avengers subsequent to the Chituari invasion will lead to a number of "wanna bes", ranging from non-powered concerned citizens putting on colorful costumes to wealthy corporations (and for-profit prisons) uilizing mechanical and biological enhancement for fun and profit. SHIELD's response could bleed into the MCU, though for now I'd prefer that the Avengers just punch Thanos.